Force Transducer: resistive - strain gauge - UDESC - CCT · Force Transducer: resistive - strain...

Force Transducer: resistive - strain gauge

►Definition: A strain gage is a sensor whose resistance varies with applied force. It converts force,

pressure, tension, weight, etc., into a change in electrical resistance which can then be measured.

L+L

W-W F F

Hooke equation:

A

F

YL

L

1 Applied force

Cross section area of the material

Elasticity module of the material

Poisson relationship:

allongitudin

ltransversa

- v = 0,5 (the volume is constant under tension);

- Metals have v values ranging from 0,3 to 0,4;

- v<0,5 (the volume increases when stretched out but decreases when

compressed).

POSTGRADUATE STUDIES ON ELECTRICAL ENGINEERING

Subject: Sensors & Transducers (4 credits)

Prof.: Dr. Pedro Bertemes Filho

► How does it work? It is based in the fact that a conductor material under tension changes

its electrical resistance. Found by Lord Kelvin in 1856. It consists of an insulating flexible

backing which supports a metallic foil pattern by a suitable adhesive, such as cyanoacrylate.

As the object is deformed, the foil is deformed, causing its electrical resistance to change. This

resistance change is related to the strain by the quantity known as the gauge factor.

►Characteristics:

High precision;

Low cost;

High linearity;

Excellent time response;

Easy installation;

Can be used immersed in water and in corrosive gases;

Can be used in telemetry;

Used for measuring weight, pressure, torque, strain,

displacement, compression, acceleration e vibration.





►The resistance of a conductor is:

LD

R

2

4





K usually vaires from 1,7 to 2,2.





►The resistance of a conductor is:

Considering :

By definition, then:

Device type Typical range of

rated capacities

Typical total

uncertainty

±% fso

Temperature sensitivity

% fso per °C

(operating range)

Strain gauge load

cells: semiconductor 1 N to 10 kN 0.2 to 1 0.2 to 0.5 (-40°C to +80°C)

Strain gauge load cells: thin film 0.1 N to 100 N 0.02 to 1 0.02 (-40°C to +80°C)

Strain gauge load cells: foil 5 N to 50 MN 0.02 to 1 0.0015 (-40°C to +80°C)

Piezoelectric crystal 1.5 mN to 120 MN 0.3 to 1 0.02 (-190°C to +200°C)

Hydraulic 500 N to 5 MN 0.25 to 5 0.02 to 0.1 (5°C to 40°C)

Pneumatic 10 N to 500 kN 0.1 to 2 0.02 to 0.1 (5°C to 40°C)

LVDT, capacitive, tuning-fork,

vibrating wire 10 mN to 1 MN 0.02 to 2 0.02 to 0.05 (-40°C to +80°C)

Magneto-elastic 2 kN to 50 MN 0.5 to 2 0.03 to 0.05 (-40°C to +80°C)

Gyroscopic** 50 N to 250 N 0.001 0.0001 (-10°C to +40°C)

Force balance** 0.25 N to 20 N 1 part in 106 0.0001 (-10°C to +40°C)





Force transducer types and their broad characteristics

►Types:

X-Y planar Rosette

Rosettes at 2 directions

Rosettes at 3 directons

Diaphragm





Base of the strain gauge

Terminal for welding the

bolding wire Grid - resistive

element (foil)

►Measuring techniques:





►Wheatstone bridge:

Gauge factor greater than 100 and a sensibility

50 times greater than the one made of metal foil





Position Transducer: types




A position transducer is any device that permits position measurement. It can either be an absolute position or a

relative (displacement sensor). Position sensors can be linear, angular, or multi-axis.

• Capacitive transducer

• Capacitive displacement sensor

• Eddy-current sensor

• Ultrasonic sensor

• Grating sensor

• Hall effect sensor

• Inductive non-contact position sensors

• Laser Doppler Vibrometer (optical)

• Linear variable differential transformer (LVDT)

• Multi-axis displacement transducer

• Photodiode array

• Piezo-electric transducer (piezo-electric)

• Potentiometer

• Proximity sensor (optical)

• Rotary encoder (angular)

• Seismic displacement pick-up

• String potentiometer (also known as string pot., string encoder, cable position transducer)

►Definition: the resistance is varied by a sliding contact which can be related by a

translation or rotation.

Position Transducer: resistive - potentiometer




►Exemple: sensor de posição do carro que contém os cartuchos de tinta em impressoras jato de tinta

iV

Vlx 0

Position of the sliding contact

Length of the resistive wire

Input voltage

Measured voltage

Characteristics:

- Range = 10 a 106 Ohms;

- This depends on the length;

- lmáx of 1 meter;

- contact noise





►Equations:

+

_ Vin Rp t

o

+

-

V0

t

o

p

po

in R

R

V

V

0

+

_ Vin Rp t

o

+

-

V0 Rm

Voltmeter

to

m

p

o

tin

R

RV

V

/1

10





►Linearity:





►Theory: are non-contact devices capable of high-resolution measurement of the position and/or

change of position of any conductive targets. They are also able to measure the thickness or density

of non-conductive materials.

►Equation:

h

AKkC

..

Capacitance (pF)

Proportionality constant

(=0,00885 for dimension in millimetres

Distance between plates

Sensor plate area (=D2/4)

Dielectric constant (K=1 if air)

Position Transducer: capacitive




Shield

Sensor

Head

Electrostatic field

Target

►Equation:

If the distance between the sensor and the target by amount of h, then:

hh

AKkCC

hh

hh

C

C

1

/Non-linear equation

The solution is to measure the reactive impedance instead of a capacitance

C

jZC

CC

jZZ CC

1

and





►Equation:

CC

CC

Z

Z

C

C

/1

/

Therefore:

h

h

Z

Z

C

C

The sensitivity of this type of sensor is given by:

AKkhCh

Z

h

ZS CC

11





►Exemple of a measuring system:





Preamplifier

Demodulator Filter Linearization

Circuit

Output

Amplifier

Voltage controlled

current source Oscillator

Power Supply

Gain

►Applications:





►Linearity:





Response voltage of a

capacitive displacement

sensor nearby its

resonance frequency

30.4 kHz using spacing

variation.

► Theory: The inductance of a wire depends on the number of turns, width of the winding or the area of the turn,

length of the winding and the permeability of the core.

Single layer coil with a cylindrical shape

KNr

L

22

Form factor

Position Transducer: inductive




►Practical measuring techniques:

Varying the permeability of the core: it uses a moving ferromagnetic core within the

winding, or a section of the winding to the fixed one;

Varying the permeability of the medium: it uses metal detectors to detect the frequency

variation from a LC oscillator and the frequency deviation measured by a FM demodulator;

Measuring the position: it uses a mutual inductance. One coil moves to each other,

which increases the coupling and the AC signal measured by the second coill.





►Operational basics: it is based on the Eddy current induced on a conducting surface when the

magnetic flux lines are intercepted by it.





Inactive

coil

Active

coil

Displacement

Target

Impedance bridge

demodulator and the

high frequency power

supply

Output

Characterisitcs:

- The coils are connected in an impedance bridge;

- The bridge output is demodulated;

- The output signal is proportional to the distance from

the target;

- The sensor sensitivity depends on the material of the

target ;

- Low output variation due to temperature;

- The sensing operation depends on the coil diameter;

- The ratio gap/diameter is equal to 0.25;

- The frequency response is between 20 and 50 kHz.





►Operational basics:

Resistivity (Ω-cm)

No

rma

lize

d o

utp

ut

in r

es

pe

ct

to A

lun

iniu

m

Perfect conductor





►Operational basics:

Magnetic materials

Non-magnetic materials

Platinum

Copper

Gold Magnesium

Tin

Aluminium Phosphorus

Brass

Nickel

Steel 1030

Steel 416

Graphite

Output for non-

magnetic materials

►Theory: É baseado na variação do acoplamento entre indutâncias, onde a saída é

proporcional ao deslocamento linear.

►Descrição: o movimento do

cilindro magnético ao longo do

núcleo sem contato, provoca a

mudança no fluxo magnético

que liga a bobina central e as

laterais.

Position Transducer: LVDT




►Esquema de ligação: as bobinas são ligadas em série e de fase oposta.

►Características:

-VS é uma excitação AC entre

50 Hz e 25 kHz;

-V0=0 quando o núcleo estiver

centrado entre as duas bobinas

laterais;

- O intervalo de operação

varia entre 2 a 150 mm,

dependendo da sensibilidade;





►Esquema de ligação: as bobinas são ligadas em série e de fase oposta.

►Circuito prático:

Oscilador 21

21

VV

VV

Filtro saída

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Force Transducer: resistive - strain gauge - UDESC - CCT · Force Transducer: resistive - strain...

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